There is a well known Medrash (anyone help with the source?) [I think on the Posuk 'Lamnatzeich Al HaShminis - A Sing on the Eight Note Instrument'] that when Moshiach comes the octave will be made up of eight notes instead of seven! Obviously this is beyond our comprehension how it is possible to fit another note in an already covered octave but that part I do not seek to understand. What I am trying to understand is why Chazal said there were 7 notes in an octave at the moment to which another note will be added!

Introduction:

An octave is just a range of pitches from point A to point B where A and B are the same note but on different pitches!

An unlimited amount of notes can be played in an octave, each slightly different from each other only detectable my machine.

Non-Western music has quarter notes in its music, and people with "perfect pitch" can listen to even more precise fractions of notes.

Western music has for Mathematical and "sounding right" reasons decided on 12 half notes in an octave! To people with perfect pitch the notes are not spot on but since for most people 12 equal half notes are good enough, that is the way it is!

A look at the piano shows 7 white keys and 5 black. See this question here about why they are split like that but after perusing the answers a few times the number seven doesnt seem all that significant. The seven white keys of the piano correspond to the major scale, starting from the C note. They are not equa-distant however, with some having a full note in between and some having a half note.

So why did Chazal say there are seven notes? Are they only counting the 7 white notes because they are the keys of the major scale of C? This style was only created later in history created by the Greeks, what did Chazal think before the Greeks came around! To quote one of the answers to the music question I linked to:

So, the western scale is based upon frequency relationships that make combinations of notes "ring" in consonance in it's purest form... like the Gregorian Chants of the Roman Church.

So, a basic "western keyboard" could be made from just these 7 notes repeated across the frequency spectrum. Look at the layout of a Greek Lyre (a harp) and that's what you will find. A sequence following the diatonic scale which sounds pleasant if you just strum across the strings due to the tuning of even multiples (adjusted by octaves).

By the way in the response to @Michoel's comment the fact that a Greek Lyre (a harp) has the main seven notes and Chazal said that we will soon have eight and the harp was the instrument of David, it appears that Chazal meant there will be an additional note, not just another repeat string!

To quote a second answer:

Note also that many cultures use a pentatonic scale. This would correspond to playing only the notes CDEGA. As explained in Qiaochu's answer, we want notes that are in small rational intervals, and particularly notes that are in small rational intervals from the tonic. Exactly which set of notes is chosen varies from culture to culture, with Western music using the 7 white keys, but many other cultures only using the 5 pentatonics.

Would the answer then be that the Seven that Chazal refer to are the Seven that sound pleasant to the ear by themselves?

@Michoel in musical terms we refer to notes as a single sound/vibration, and chords as a few notes rightly played at the same time creating a different sound. I assume it must be referring to notes and not chords because there are many more then 8 chords, chords are there to harmonise the notes being played!
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YehudaOct 4 '12 at 10:19

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I can help with the music part but not the midrash part. A western scale has seven (named) tones. It may have accidentals (half-steps out of the key), which are temporary alterations of one of those seven notes, but in any given piece of music that doesn't modulate, you'll see ABCDEFG in some form (depending on key/mode) but not, say, A and A-flat both as core notes. AFAIK this holds for Arabic music with its quarter-tones too. There are lots of different scales and modes, but they all revolve around 7 notes.
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Monica Cellio♦Oct 4 '12 at 13:07